Solving Multi-Step Equations Thinker Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $190. How much does each person have? Ana, $114; Ben, $57; Clio, $19

COMMON CORE #9B To solve a multi-step equation, including (1)word problems (2)combining like terms (3)Distributive Property

Combining Like Terms Solve 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract 4 from both sides. 11x = 33 33 11 11x = Divide both sides by 11. x = 3

Check The Answer!  Check 8x + 6 + 3x – 2 = 37 8(3) + 6 + 3(3) – 2 = 37 ? Substitute 3 for x. 24 + 6 + 9 – 2 = 37 ? 37 = 37 ? 

You Work This One Solve 6x + 5 + 4x – 13 = 42 10x - 8 = 42 Combine like terms. +8 +8 Add 8 to both sides. 10x = 50 50 10 10x = Divide both sides by 10. x = 5

Now Check It  Check 6x + 5 + 4x – 13 = 42 6(5) + 5 + 4(5) – 13 = 42 Substitute 5 for x. 30 + 5 + 20 – 13 = 42 42 = 42 

Using The Distributive Property Solve 4(x – 6) + 7 = 11 4(x – 6) + 7 = 11 Distributive Property 4(x) – 4(6) + 7 = 11 Simplify by multiplying: 4(x) = 4x and 4(6) = 24. 4x – 24 + 7 = 11 4x – 17 = 11 Simplify by adding: –24 + 7 = 17. + 17 +17 Add 17 to both sides. 4x = 28 Divide both sides by 4. 4 x = 7

Now Check It! Check 4(x – 6) + 7 = 11 4(7 – 6) + 7 = 11 Substitute 7 for x 4(1) + 7 = 11 4 + 7 = 11 11 = 11

You Try It Solve 8(x + 2) - 3 = 5 8(x + 2) - 3 = 5 Distributive Property 8(x) + 8(2) - 3 = 5 Simplify by multiplying: 8(x) = 8x and 8(2) =16 8x + 16 - 3 = 5 8x + 13 = 5 Simplify by adding: 16 - 3 = 13 - 13 - 13 Subtract 13 from both sides. 8x = -8 Divide both sides by 8. 8 x = -1

You Check It! Check 8(x + 2) - 3 = 5 8(-1 + 2) - 3 = 5 Subsitute -1 for x 8(1) - 3 = 5 8 - 3 = 5 5 = 5

PRACTICE PROBLEMS x = 6 Solve 1. 6x + 3 – 2x + 6 = 33 y = 1 Solve 1. 6x + 3 – 2x + 6 = 33 2. 8(y + 2) + 5 = 29 3. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate? 40h + 2(12h) = 544 $8.50